In pattern recognition machines, such as that described in patent application Ser. No. 07/770267, filed Oct. 3, 1991, and assigned to Applicant's assignee, it is usual to store large amounts of prototype patterns and compare them to a given example or unknown input symbol for identification. In several pattern comparison processes using common algorithms, such as K-nearest Neighbor (KNN), Parzen windows, and radial basis function (RBF), the comparison is performed by generating a distance measure, for example the Euclidean distance, between patterns and prototypes. The KNN and Parzen windows algorithms are described in the book, Pattern Classification and Scene Analysis, by Duda and Hart, 1973; and the RBF algorithm is described in the article, "Multivariate Functional Interpolation and Adaptive Networks," appearing in Complex Systems, by D. S. Broomhead and D. Lowe, which are hereby incorporated by reference.
According to these, and related algorithms, the several prototypes which have the smallest distances from the example each cast a vote. The voting determines the class of the example. Variations on the voting scheme and on how the distance measure is used account for the difference between the KNN, Parzen windows, RBF and other distance-based classification algorithms.
These classification methods find important applications in optical character recognition. For example, these methods are usefully employed in machines for making accurate classifications as to the identity of letters and numbers in the address block of envelopes being processed at a postal service sorting center. In these machines, it is necessary that the classifier recognize accurately the many shapes and sizes in which each letter or number are formed in script placed on the envelopes by postal service users.
Thus, a desirable property of a pattern recognition machine is that its output be invariant with respect to certain small transformations of its input. That is, some transformations of a meaningful pattern, such as an alphanumeric symbol, will not affect the interpretation of the pattern by a human observer. A comparison scheme that is invariant to such transformations can operate with greater economy and speed than comparison schemes that require exhaustive sets of prototypes. By way of example, transformations of alphanumeric patterns that are of interest in this regard include translation, rotation, scaling, hyperbolic deformations, line thickness changes, and grey-level changes.
A new scheme for comparing prototypes to examples in recognition machines which practice the KNN, Parzen window and RBF algorithms has been described in the U.S. Pat. No. 5,422,961 and assigned to Applicant's assignee, hereby incorporated by reference. This comparison scheme is invariant with respect to a selected set of small transformations of the prototypes or the examples. The transformations are expressed using only a few operators. A distance function is used that allows accurate choices to be made, as to the class of the example, that are invariant to small transformations of either the example or the prototype.
The small transformations of interest are expressed by calculating the derivative of the transformed image with respect to the parameter that controls the transformation. This directional derivative is used to generate the computational representation of the transformation of interest.
The transformation of interest (i.e., with respect to which invariance is desired) can be efficiently expressed by using the tangent vectors to the surface of transformation. Any desired number of possible invariances can be included in any particular recognition process.
This comparison scheme can appreciably enhance the speed and accuracy with which, e.g., alphanumeric symbols are recognized. However, an example pattern, to be recognized, must be compared with each of the stored prototypes.
According to practices of the prior art, all of these comparisons are performed at the same level of detail. This is inherently inefficient because a reduced level of detail in the comparisons may suffice to determine how close the example pattern is to many of the prototypes.